We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.
Fate of the Hoop Conjecture in Quantum Gravity / Anza, F.; Chirco, G.. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 119:23(2017). [10.1103/PhysRevLett.119.231301]
Fate of the Hoop Conjecture in Quantum Gravity
Chirco G.
2017
Abstract
We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.